Question

Determine if r(x) is continuous at 1.26? Use limits in your explanation of why this functions is or is not continuous at 1.26

Answer 1

Given:

`R(x)\text{ = }(x^3-x^2+x-1)/(x^4-x^3+2x-2)`

A function f(x) is continuous at a point x=c :

`\lim_(x\to c)\text{ f\lparen x\rparen = f\lparen c\rparen}`

First, let us take the limit:

`=\lim_(x\to\:1.26)\left((x^3-x^2+x-1)/(x^4-x^3+2x-2)\right)`

Plug in the values x = 1.26

`\begin{gathered} =(1.26^3-1.26^2+1.26-1)/(1.26^4-1.26^3+2\cdot \:1.26-2) \\ =0.64683 \end{gathered}`

Now, let us find R(1,26):

`R(1.26)\text{ = 0.6468}`

Hence, we can conclude that R(x) is continuous at x = 1.26